In cardiovascular flows, blood transport has been revealed using the Lagrangian coherent structures (LCS). Through a geometric approach, the extracted LCS highlight mixing, stagnation, and elevated shear stress regions. In geophysical flows, graph-theoretic approaches are used to represent fluid transport as a complex flow network. By using classical graph measures, one can extract the LCS along with direct measures of local dispersion and mixing. Also, from the adjacency matrix of the flow network, we can identify the coherent sets in the flow where the fluid within each set is minimally mixed with that in other sets. Notably, the geometric approach can only detect the borders of such regions. This study shows the first application of complex networks analysis to instantaneous planar velocity fields (acquired via PIV) downstream different arrangements of healthy and repaired mitral valves. Using the in- and out-degrees of the transport matrix, the instantaneous local mixing and dispersion are highlighted. Moreover, the LCS are revealed by computing the discrete finite time entropy of the network. Finally, the flow transport matrix is partitioned using a fuzzy c-means clustering algorithm to reveal the flow coherent sets which can better reveal fluid transport mechanisms.